(1) Field of the Invention
This invention relates to an apparatus, method, and program for designing a mask and a method for fabricating semiconductor devices by the use of such a mask and, more particularly, to an apparatus, method, and program for designing a mask in which an exposure pattern or a pattern of physical shape formed on a semiconductor substrate is calculated with a filter and in which a mask is designed on the basis of calculated results and a method for fabricating semiconductor devices by the use of such a mask.
(2) Description of the Related Art
Highly accurate large scale integrated circuit (LSI) patterns which have been used in recent years require minute pattern formation technologies and highly accurate pattern formation technologies. To form minute patterns, that is to say, patterns smaller than or equal to light wavelengths used in exposure systems, phase shifts have been applied. To form highly accurate patterns, optical proximity corrections (OPCs) have been applied.
With an OPC, a correction pattern for mask pattern data is made to optically correct a pattern on a mask (or reticle) and to transfer a desired image onto a wafer. A rule-based method and simulation-based method are widely known as a method for making a correction pattern. The simulation-based method is suitable for highly accurate LSI patterns and it will be necessary in the future to apply the simulation-based method to all LSI chips.
FIG. 16 is a view for describing a way of adding an OPC in a conventional simulation-based method. In FIG. 16, the structure of an exposure system for transferring a pattern formed on a mask 12 onto a wafer 14 in an exposure process is shown in an area enclosed by a dashed line.
As shown in FIG. 16, the exposure system includes a light source 10, an illumination lens 11, the mask 12, and a projection lens 13 and transfers the pattern formed on the mask 12 onto the wafer (semiconductor substrate) 14.
The light source 10 irradiates ultraviolet rays, electron beams, or the like.
The illumination lens 11 makes ultraviolet rays or electron beams irradiated from the light source 10 converge on an area on the mask 12 to be transferred.
The mask 12 is fabricated by forming a light shielding film of chromium corresponding to a circuit pattern on a silica substrate. The mask 12 shuts out or transmits ultraviolet rays or electron beams which passed through the illumination lens 11 according to the circuit pattern.
The projection lens 13 makes light which passed through the mask 12 converge on a predetermined area on the wafer 14.
The wafer 14 is, for example, a silicon wafer coated with photo resist.
Now, a way of adding an OPC in the simulation-based method will be described with reference to FIG. 16.
It is assumed that a mask pattern 12a shown at the top of FIG. 16 is transferred onto the wafer 14. In this case, it is desirable that an exposure pattern 14a transferred onto the wafer 14 should be more similar to the mask pattern 12a. But in reality the exposure pattern 14a on the wafer 14 does not match the mask pattern 12a due to light diffraction and the like and becomes dim as shown in FIG. 16.
Therefore, an OPC is added to the mask pattern 12a to make the exposure pattern 14a more similar to the mask pattern 12a. However, to find the most effective OPC to be added, the following way must be used. The mask 12 is actually fabricated and an OPC is added or corrected according to a result obtained by using it. Then this addition or correction is repeated.
However, fabricating the mask 12 is troublesome. Therefore, with the above simulation-based method, the exposure pattern 14a obtained by transferring the mask pattern 12a formed on the mask 12 onto the wafer 14 is simulated with a computer or the like and an OPC is added or corrected according to the result of the simulation.
Conventionally, the exposure pattern 14a is calculated by performing fast Fourier transform (FFT) on the mask pattern 12a formed on the mask 12. Then an OPC is added to the mask pattern 12a or an OPC added to the mask pattern 12a is corrected so that the exposure pattern 14a will form a desired shape.
By the way, FFT operations involve complex operations, so it takes a long time to perform a process.
Therefore, if the simulation-based method is applied to an entire LSI chip at a high integration level, it will take a very long time to perform a process, resulting in a long development period.